SOLUTION: A homeowner is installing a swimming pool. He wants the length 4 feet longer than the width then he wants to install a concrete walkway around it. The walkway needs to be 3 ferry w
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Question 755389: A homeowner is installing a swimming pool. He wants the length 4 feet longer than the width then he wants to install a concrete walkway around it. The walkway needs to be 3 ferry wide with a total area of 300 sq feet. What should the dimensions of the pool be Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A homeowner is installing a swimming pool.
He wants the length 4 feet longer than the width.
Then he wants to install a concrete walkway around it.
The walkway needs to be 3 feet wide, with a total area of 300 sq feet.
What should the dimensions of the pool be?
:
Let x = the width of the pool
then
(x+4) = the length of the pool
:
The walkway to be 3' wide therefore 6' will added to the pool dimensions.
the overall dimensions will be
W: (x+6)
L: (x+4+6) = (x+10)
:
Total area - pool area = walkway area
[(x+10)*(x+6)] - [x(x+4)] = 300
FOIL
(x^2 + 16x + 60) - (x^2+4x) = 300
remove brackets combine like terms
x^2 - x^2 + 16x - 4x + 60 = 300
12x = 300 - 60
12x = 240
x = 240/12
x = 20 ft is the width of the pool
then
20 + 4 = 24 ft is the length of the pool
:
;
You can see if this checks out, do the math:
Total area - pool area = walkway area
[(20+10)*(20+6)] - [24*20] = 300
